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A hybrid machine-learning and optimization method to solve bi-level problems

Journal article
Authors Saeed Asadi Bagloee
Mohsen Asadi
Majid Sarvi
Michael Patriksson
Published in Expert Systems with Applications
Volume 95
Pages 142-152
ISSN 0957-4174
Publication year 2018
Published at Department of Mathematical Sciences
Pages 142-152
Language en
Links https://doi.org/10.1016/j.eswa.2017...
Keywords Bi-level, Discrete network design problem, Integer linear programming, Machine learning, Supervised learning
Subject categories Optimization, systems theory, Other Mathematics

Abstract

© 2017 Elsevier Ltd Bi-level optimization has widespread applications in many disciplines including management, economy, energy, and transportation. Because it is by nature a NP-hard problem, finding an efficient and reliable solution method tailored to large sized cases of specific types is of the highest importance. To this end, we develop a hybrid method based on machine-learning and optimization. For numerical tests, we set up a highly challenging case: a nonlinear discrete bi-level problem with equilibrium constraints in transportation science, known as the discrete network design problem. The hybrid method transforms the original problem to an integer linear programing problem based on a supervised learning technique and a tractable nonlinear problem. This methodology is tested using a real dataset in which the results are found to be highly promising. For the machine learning tasks we employ MATLAB and to solve the optimization problems, we use GAMS (with CPLEX solver).

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